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<span class="kw">let </span><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_2.html#K2" title="FLANG_2:func.2">?</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="flang_2.html#K2" title="FLANG_2:func.2">?</a> </span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_2.html#K2" title="FLANG_2:func.2">?</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_2.html#K2" title="FLANG_2:func.2">?</a> </span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  )</span><br/>



<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_2.html#K2" title="FLANG_2:func.2">?</a>  = 
<span class="p1"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="flang_2.html#T76" target="_self" title="FLANG_2:th.76">Th76</a></span>
<br/>.= 
<font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="flang_1.html#T49" title="FLANG_1:th.49">FLANG_1:49</a>, <a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_2.html#K2" title="FLANG_2:func.2">?</a> </span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_2.html#K2" title="FLANG_2:func.2">?</a> </span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  = 
<span class="p1">(<span class="default"><span class="p2"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><span class="p3">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="flang_2.html#T76" target="_self" title="FLANG_2:th.76">Th76</a></span>
<br/>.= 
<font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="flang_1.html#T49" title="FLANG_1:th.49">FLANG_1:49</a>, <a class="ref" href="flang_1.html#T69" title="FLANG_1:th.69">FLANG_1:69</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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